Using all-atom molecular dynamics simulations in water environment, it was possible to demonstrate spontaneous and tight encapsulation of glucose oxidase (GOx) dimer by graphene 7 nm x 7 nm sheets linked together by linkers of different width and forming a flower-like or cross-like shapes. The partially overlapping graphene sheets compacted the structure of GOx dimer, bringing the monomers much closer to one another. We found that the most complete wrapping of the enzyme was achieved for the cross-like graphene. Encapsulation can be a useful way to obtain a large contact surface. However, an exceptionally tight binding by the graphene can also influence the positions of amino acids in the enzyme binding site resulting in less efficient catalytic reaction. Furthermore, such extensive encapsulation could block the access of the substrate to the active site of the enzyme. Contrary, a partial encapsulation by graphene using nano-sheets caused only small distortions of GOx structure while the contact surface with graphene was high.